A method is presented that compensates for manipulator end-point errors in order to achieve very high position accuracy. The measured end-point error is decomposed into generalized geometric and elastic error parameters that are used in an analytical model to calibrate the system as a function of its configuration and the task loads, including any payload weight. The method exploits the fundamental mechanics of serial manipulators to yield a non-iterative compensation process that only requires the identification of parameters that are function only of one variable. The resulting method is computationally simple and requires far less measured data than might be expected. The method is applied to a six degrees-of-freedom (DOF) medical robot that positions patients for cancer proton therapy to enable it to achieve very high accuracy. Experimental results show the effectiveness of the method.